Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions

The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.     

Behavior of a polymer chain immersed in a binary mixture of solvents

The behavior of a polymer chain immersed in a binary solvent mixture is investigated via a single-polymer simulation using an effective Hamiltonian, where the solvent effects are taken into account through a density-functional theory for polymer-solvent admixtures. The liquid-liquid phase separation of the binary solvent mixture is modeled as that of a Lennard-Jones binary fluid mixture with weakly attractive interactions between the different components. Two types of energetic preferences of the polymer chain for the better solvent-(A) no preferential solvophilicity and (B) strong preferential solvophilicity-are employed as polymer-solvent interaction models. The radius of gyration and the polymer-solvent radial distribution functions are determined from the simulations of various molar fractions along an isotherm slightly above the critical temperature of the liquid-liquid phase separation. These quantities near the critical point conspicuously depend on the strength of the preferential solvophilicity. In the case where the polymer exhibits a strong preferential solvophilicity, a remarkable expansion of the polymer chain is observed near the critical point. On the other hand, in the case where the polymer has no preferential solvophilicity, no characteristic variation of the polymer conformation is observed even near the critical point. These results indicate that the expansion of a polymer chain enhances the local phase separation around it, acting as a nucleus of demixing in the vicinity of the critical point. This phenomenon in binary solvents near the liquid-liquid critical point is similar to the expansion of the polymer chain in one-component supercritical solvents near the liquid-vapor critical point, which we have reported [T. Sumi and H. Sekino J. Chem. Phys. 122, 194910 (2005)].     

Collapse transitions of a supersized neutral chain due to irreversibly adsorbed small colloidal particles

 We performed Monte Carlo simulations to study the destabilization processes of large neutral and flexible polymer chains due to irreversibly adsorbed colloidal particles attached to the chains like beads on a necklace. The particles are modeled as charged spherical units which interact with each other via repulsive electrostatic and attractive van der Waals (vdW) potentials. The usual Monte Carlo search procedure is extended and carefully checked to completely sample the chain conformational space and achieve dense conformations in the limit of both strong attractive and repulsive interaction potentials. Configurational properties, such as the radius of gyration, the end-to-end length, and the Kuhn length, are calculated as a function of the intensity of the vdW interactions and ionic strength values. It is observed that chains exhibit a new range of possible conformations compared to the classical random walk and self avoiding walk chains or polyelectrolytes. In the limit of low salt concentration, by gradually increasing vdW interactions, chains undergo a cascade of transitions from extended structures to dumbbells, from dumbbells to pearl necklaces, and from pearl necklaces to collapsed coils. Because of strong competition between the vdW and electrostatic forces, the distance along the chain between the interacting particles, and the sampling limitations, these transitions are found to sample metastable domains and to depend on the initial conformations. To gain insight into the spatial organization of the collapsed conformations, the pair correlation functions of both monomers and particles are calculated. It is shown that collapsed conformations which are the result of strong particle–particle interactions exhibit two distinct parts: a hard core mainly composed of particles and a surrounding polymeric shell composed of loops and tails. Possible effects of such a collapsed transition on the kinetics of flocculation of a mixture containing large flexible chains and small adsorbing colloidal particles are discussed. Received: 26 July 1999 Accepted in revised form: 9 November 1999     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

Molecular dynamics simulations of polyelectrolyte-polyampholyte complexes. Effect of solvent quality and salt concentration

Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.     

Effects of chain conformation and chain length on degree of aggregation in assembled particles of conjugated polymer in solvents–nonsolvent: A spectroscopic study

This article explores photophysical properties and aggregation behaviors of conjugated polymer, poly[2‐methoxy, 5‐(2′‐ethylhexyloxy)‐1,4‐phenylenevinylene](MEH?PPV), in various solvent–nonsolvent systems by utilizing UV/vis absorption and photoluminescence (PL) spectroscopy. The isolated chains of MEH‐PPV dispersed in solvents including dichloromethane, chloroform, and tetrahydrofuran adopt either extended or collapsed conformations depending on local polymer–solvent interactions. Aggregation of the MEH‐PPV in these solvents is induced by addition of a poor solvent, cyclohexane. The formation of aggregates is indicated by the appearance of distinct red‐shift peaks in the absorption and PL spectra. The degree of aggregation in each solvent–nonsolvent system is compared by means of absorbance and PL intensity of the aggregate bands. In early stage of the aggregation, the amount of aggregates in system is controlled by the solubility of polymer. When the polymer chains are forced to densely pack within assembled particles by increasing ratio of cyclohexane to 99 v/v %, the conformation of individual chain plays important role. We have found that the extended chains facilitate the aggregation in the assembled particles. Increasing chain length of polymer promotes the aggregation in early stage and densely packed particles. Size distribution of the assembled particles is also found to depend on the choice of solvent. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 894–904, 2010     

Mean‐field‐theory for polymers in mixed solvents. Thermodynamic and structural properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the mixed solvent is near criticality without solute, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer‐solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes phase transition from a swollen state to an unperturbed state or even takes a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein‐Zernike series expansion.     

Conformational behavior of polymers adsorbed on nanotubes

The importance of hydrophobic interactions in determining polymer adsorption and wrapping of carbon nanotubes is still under debate. In this work, we concentrate on the effect of short-ranged weakly attractive hydrophobic interactions between polymers and nanotubes (modeled as an infinitely long and smooth cylindrical surface), neglecting all other interactions apart for chain flexibility. Using coarse-grained Monte Carlo simulation of such simplified systems, we find that uniform adsorption and wrapping of the nanotube occur for all degrees of chain flexibility for tubes with sufficiently large outer radii. However, the adsorbed conformations depend on chain stiffness, ranging from randomly adsorbed conformations of the flexible chain to perfect helical or multihelical conformations (in the case of more concentrated solutions) of the rigid chains. Adsorption appears to occur in a sequential manner, wrapping the nanotube nearly one monomer at a time from the point of contact. Once adsorbed, the chains travel on the surface of the cylinder, retaining their helical conformations for the semiflexible and rigid chains. Our findings may provide additional insight to experimentally observed ordered polymer wrapping of carbon nanotubes.     

Chain conformations of block copolymers

An analytical theory of block copolymer conformations is developed for systematically studying the effects of the chain length, chain architecture, and segment interactions. The main results obtained for AB diblock and ABA triblock chains are as follows: (i) In the absence of AA and BB interactions, both diblock and triblock chains collapse to a dense form if the AB interaction is attractive. In the collapsed coil form, the mean-square end-to-end distance 〈R²〉 is proportional to the square root of the number of segments n^1/2. (ii) The diblock chain has a dumbbell form if AA and BB interactions are attractive and AB interaction repulsive, but the triblock chain collapses. In the dumbbell form, 〈R²〉 is proportional to n.     

The Correlation Functions of a Suspension of Large Particles in Amorphous Polybutadiene: A Molecular Dynamics Simulation Study

The correlation functions of a suspension of Lennard-Jones large particles in a model 1,4-cis-polybutadiene solvent have been investigated by molecular dynamics simulations. We present the effects of temperature, the degree of polymerization, and the solvent/large particle density on the effective interactions between the large particles and the solvent. It is found that as the temperature increases, the structure between solvent-solvent, solvent-large particle, and large-large particle decreases. Additionally, as the bulk density or the chain length is increased, the attractive part of the large-large interaction becomes weaker and small. We believe that in part, this is due to the polymer having collapsed onto itself and entangling the large particles and lessening their interaction until they are actually in contact. Increasing the length of the polymer also entangles the large particles. However, we believe that this may be a general feature that is a characteristic of a polymer solvent containing macroscopically large colloidal particles even though entanglement should be of less significance. Copyright 2000 Academic Press.     

A Monte Carlo study of the coil-to-globule transition of model polymer chains near an attractive surface

When a polymer chain in solution interacts with an atomically smooth solid substrate, its conformational properties are strongly modified and deviate substantially from those of chains in bulk. In this work, the interplay of two competing transitions that affect the conformations of polymer chains near an energetically attractive surface is studied by means of Monte Carlo simulations on a cubic lattice. The transition from an extended to a compact conformation of a polymer chain near an attractive wall, as solubility deteriorates, exhibits characteristics akin to the “coil-to-globule” transition in bulk. An effective θ-temperature is determined. Its role as the transition point is confirmed in a variety of ways. The nature of the coil-to-compact transition is not qualitatively different from that in the bulk. Adsorbed polymer chains may assume “globular” or “pancake” configurations depending on the competition among adsorption strength, cohesive energy, and entropy. In a very relevant range of conditions, the dependence of the adsorbate thickness on chain-length is intermediate between that of 3-d (“semidroplets”) and 2-d (“pancake”) objects. The focus of this study is on rather long polymer chains. Several crucial features of the transitions of the adsorbed chains are N-dependent and various aspects of the adsorption and “dissolution” process are manifested clearly only at the “long chain” limit. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2462–2476, 2009     

Sedimentation of aggregating colloids

We investigate the combined effects of gravity, attractive interactions, and brownian motion in suspensions of colloidal particles and nonadsorbing polymer. Depending on the effective strength of gravitational forces, resulting from a density mismatch between the colloids and the solvent, and the magnitude and range of the depletion interactions induced by the polymer, sedimentation in these suspensions can result in an equilibrium structure or a kinetically arrested state. We employ large-scale molecular dynamics simulations to systematically classify the different regimes that arise as a function of attraction strength and gravitational stress. Whereas strong attractions lead to cluster aggregation and low-density arrested states, moderate attractions can enhance crystallization of the colloidal particles in the sediment. We make direct comparisons to experimental results to infer general conclusions about the mechanisms leading to mechanically stable sediments.     

Effect of the Solvent on the Conformation of Isolated MEH‐PPV Chains Intercalated Into SnS2

Photophysical processes in conjugated polymers are influenced by two competing effects: the extent of excited state delocalization along a chain, and the electronic interaction between chains. Experimentally, it is often difficult to separate the two because both are controlled by chain conformation. Here we demonstrate that it is possible to modify intra‐chain delocalization without inducing inter‐chain interactions by intercalating polymer monolayers between the sheets of an inorganic layered matrix. The red‐emitting conjugated polymer, MEH‐PPV, is confined to the interlayer space of layered SnS₂. The formation of isolated polymer monolayers between the SnS₂ sheets is confirmed by X‐ray diffraction measurements. Photoluminescence excitation (PLE) and photoluminescence (PL) spectra of the incorporated MEH‐PPV chains reveal that the morphology of the incorporated chains can be varied through the choice of solvent used for chain intercalation. Incorporation from chloroform results in more extended conformations compared to intercalation from xylene. Even highly twisted conformations can be achieved when the incorporation occurs from a methanol:chloroform mixture. The PL spectra of the MEH‐PPV incorporated SnS₂ nanocomposites using the different solvents are in good agreement with the PL spectra of the same solutions, indicating that the conformation of the polymer chains in the solutions is retained upon intercalation into the inorganic host. Therefore, intercalation of conjugated polymer chains into layered hosts enables the study of intra‐chain photophysical processes as a function of chain conformation.     

Structure and Dynamics of Confined Polymer Melts from Attractive Interaction to Repulsive Interaction Between Polymer and Smooth Wall

We studied the static and dynamic properties of unentangled polymer chains which have a variable strength of interaction with the confining smooth walls by means of the lattice Monte Carlo simulation based on the bond-fluctuation model, that is, investigated the wall-polymer interactions which systematically vary from attraction to repulsion. A critical value of attractive potential(ε_wc) is found to be -0.6k_BT, and only below it can the adsorption layer of monomers be formed near the wall. At the critical point of attraction ε_wc, attractive interaction counterba- lances the wall-polymer excluded volume effect, which minimizes the confinement effects on both chain dimension and mobility. Influences on both chain dimension and mobility increase with the increasing of either attraction or repulsion imposed by the walls. Despite of the nature and strength of the wall-polymer interaction, with the decrease of film thickness, configurations more parallelly aligned and flattened are adopted by confined chains, and a systematic trend of deceleration is found. Variations of chain dynamics with both film thickness and wall-polymer interaction can be well explained by the corresponding changes in the confinement of the nearest-neighboring particles that surround the chains. Besides, the thickness of the interfacial layer inside polymer films, where chains adopt a flattened “pancake” shape, is about two times the bulk radius of gyration and independent of the wall-polymer interaction.     

Conformational properties of rigid-chain amphiphilic macromolecules: The phase diagram

The coil-globule transition in rigid-chain amphiphilic macromolecules was studied by means of computer simulation, and the phase diagrams for such molecules in the solvent quality-persistence length coordinates were constructed. It was shown that the type of phase diagram depends to a substantial extent on the degree of polymerization of a macromolecule. Relatively short amphiphilic macromolecules in the poor-solvent region always form a spherical globule, with the transition to this globule involving one or two intermediate conformations. These are the disk globule if the Kuhn segment is relatively large and the string of spherical micelles or the disk globule in the case of relative flexible chains. The phase diagram of a long rodlike amphiphilic chain turned out to be even more complex. Namely, three characteristic regions were distinguished in the region of a poor solvent, depending on the chain rigidity: the region of a cylindrical globule without certain order in the main chain, the region of the cylindrical globule with blobs having the collagen ordering of the chain, and the region of coexistence of collagen-like and toroidal globules. In the intermediate transitional region, not only conformations of strings of spherical micelle beads but also the necklace conformations in which the polymer chain in each bead has collagen ordering can occur in this case.     

Mean field theory for the intermolecular and intramolecular conformational transitions of a single flexible polyelectrolyte chain

The diMarzio theory has been extended to elucidate the intermolecular and intramolecular phase segregations of a single flexible chain polyelectrolyte in dilute salt-free solutions. At the long chain limit, this theory yields the formalism obtained from the more sophisticated Edward Hamiltonian for polyelectrolyte problems. The calculated phase diagram exhibits the features of a first-order phase transition, with continuous and discontinuous transitions separated by a critical point. Under the discontinuous transition, the polyelectrolyte chain exhibits coexistent expanded and collapsed conformational states, same as intermolecular phase segregation. For a limiting long chain, the mean chain size at critical point is roughly 90% of the size of an ideal chain. Such a result implies that partial contraction within a chain molecule is required to collapse a flexible polyelectrolyte chain. Moreover, the theory predicts that for a longer chain, intramolecular segregated conformations differ significantly from intermolecular segregated conformations, but the difference becomes small for shorter chains. Besides, the charge needed to induce intramolecular segregation is smaller than that of intermolecular segregation for a given chain length. These findings are consistent with previous literature results.     

Linear chain surfactants at a planar interface: a comparative Monte Carlo study of several lattice models

Linear chain surfactants in a densely packed arrangement (such as alkane chains in lipid monolayers in the “uniform tilt” structures) are described by a crude coarse-grained model where the endgroups grafted on the interface form a regular lattice and the chains are described by the bond fluctuation model with chains containing N = 4 effective monomers only. Square-well interactions between the monomers are studied for both the attractive and repulsive case for three choices of the interaction range. None of these models exhibits a structure with uniform tilt. For attractive interactions the last bond has a strong tendency to fold back thus leading to a very high density close to the interface. Only when an intrachain-potential favoring stiff chain configurations also is included one can obtain configurations with uniform tilt order. Although related models (with much longer chain lengths and lower grafting densities) are very useful for the study of polymer brushes, the present case of very short chains in a high-density state clearly is plagued by various lattice artefacts and it is concluded that for modelling linear chain surfactants one should use an off-lattice model even on a coarse-grained level.     

Conformation and solvation structure for an isolated n-octadecane chain in water, methanol, and their mixtures

Configurational-bias Monte Carlo simulations in the isobaric-isothermal ensemble (T = 323 K and p = 10 atm) were carried out to probe structural properties of an isolated n-octadecane chain solvated in water, methanol, water-rich, or methanol-rich mixtures and, for comparison, of an isolated chain in the gas phase and for neat liquid n-octadecane. The united-atom version of the TraPPE (transferable potentials for phase equilibria) force field was used to represent n-octadecane and methanol and the TIP-4P model was used for water. In all six environments, broad conformational distributions are observed and the n-octadecane chains are found to predominantly adopt extended, but not all-trans conformations. In addition, a small fraction of more collapsed conformations in which the chain ends approach each other is observed for aqueous hydration, the water-rich solvent mixture and the gas phase, but the simulation data do not support a simple two-state picture with folded and unfolded basins of attraction. For chains in these three "poor" solvent environments, the dihedral angles near the center of the chain show an enhancement of the gauche population. The ensemble of water-solvated chains with end-to-end contacts is preferentially found in a U-shaped conformation rather than a more globular state. An analysis of the local solvation structures in the water-methanol mixtures shows, as expected, an enrichment of the methyl group of methanol near the methylene and methyl segments of the n-octadecane chain. Interestingly, these local bead fractions are enhanced by factors of 2.5 and 1.5 for methyl and methylene segments reflecting the more hydrophobic nature of the former segments.